Question

Noir drove from the Dead Sea up to Amman, and her altitude increased at a constant rate. When she began driving her altitude was 400 meters below sea level. When she arrived in Amman 2 hours later, her altitude was 1000 meters above sea level. Let y represent noir’s altitude in meters relative to sea level after x hours.

Answer 1

y(x) = -400 m + (700 m/hr)x

Explanation:

Let y = 0 represent sea level. Noir's initial altitude was -400 m. In two hours she went from -400 m to +1000 m, a positive change of 1400 m. Thus, the rate of ascent was m = slope = (change in altitude) / (change in time), or

rate of ascent = 1400/2 m/hr = 700 m/hr

Thus, an equation describing her altitude relative to sea level after x hours is

y(x) = -400 m + (700 m/hr)x, where x is the number of hours of driving completed. This formula correctly predicts the altitude after two hours:

y(2) = -400 m + (700 m/hr)(2 hr) = 1000 m above sea level.